Question

if these two figures are similar, what is the measure of the missing angle? the first triangle has angles 38°, 104°, 38°. the second triangle has a missing angle ?.

Explanation:

Step1: Recall properties of similar triangles

Similar triangles have corresponding angles equal. Also, the sum of angles in a triangle is \(180^\circ\).

Step2: Identify corresponding angles

In similar triangles, corresponding angles are equal. The first triangle has angles \(38^\circ\), \(38^\circ\), and \(104^\circ\). The second triangle will have the same set of angles (since they are similar).

Step3: Calculate the missing angle (if needed, but here we can see the angle corresponding to \(104^\circ\) is the missing one as the other two angles in the second triangle should correspond to \(38^\circ\) each, so the missing angle is equal to \(104^\circ\) because of the similarity (corresponding angles are equal) and also we can verify by angle sum: Let the missing angle be \(x\). For a triangle, \(38^\circ + 38^\circ+ x= 180^\circ\)? Wait no, wait the first triangle: \(38 + 38+ 104 = 180\) (38+38=76, 76+104=180). So the second triangle, since it's similar, the angles must be the same. So the angles in the second triangle should be \(38^\circ\), \(38^\circ\), and \(104^\circ\). So the missing angle is \(104^\circ\). Wait, maybe I misread. Wait the first triangle has angles 38, 38, 104. The second triangle: let's check the angle sum. If two angles are 38 each, then the third is 180 - 38 -38 = 104. So yes, the missing angle is 104 degrees.

Answer:

\(104^\circ\)